LMFDB - Embedded newform 4110.2.a.bb.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4110,2,Mod(1,4110)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4110, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4110.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4110 = 2 \cdot 3 \cdot 5 \cdot 137 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4110.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.8185152307$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1900864.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 9x^{3} + 16x^{2} + 14x - 16 $ x^5 - 2x^4 - 9x^3 + 16x^2 + 14x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.783314$ of defining polynomial
Character	$\chi$	$=$	4110.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.38642 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.38642 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -0.416420 q^{11} -1.00000 q^{12} -3.21926 q^{13} +4.38642 q^{14} +1.00000 q^{15} +1.00000 q^{16} +0.742608 q^{17} +1.00000 q^{18} +6.16973 q^{19} -1.00000 q^{20} -4.38642 q^{21} -0.416420 q^{22} -4.99375 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.21926 q^{26} -1.00000 q^{27} +4.38642 q^{28} -1.25739 q^{29} +1.00000 q^{30} +0.298097 q^{31} +1.00000 q^{32} +0.416420 q^{33} +0.742608 q^{34} -4.38642 q^{35} +1.00000 q^{36} +11.2795 q^{37} +6.16973 q^{38} +3.21926 q^{39} -1.00000 q^{40} -1.15021 q^{41} -4.38642 q^{42} +11.2537 q^{43} -0.416420 q^{44} -1.00000 q^{45} -4.99375 q^{46} +4.99375 q^{47} -1.00000 q^{48} +12.2407 q^{49} +1.00000 q^{50} -0.742608 q^{51} -3.21926 q^{52} +1.72522 q^{53} -1.00000 q^{54} +0.416420 q^{55} +4.38642 q^{56} -6.16973 q^{57} -1.25739 q^{58} +3.60122 q^{59} +1.00000 q^{60} +0.959294 q^{61} +0.298097 q^{62} +4.38642 q^{63} +1.00000 q^{64} +3.21926 q^{65} +0.416420 q^{66} -14.6297 q^{67} +0.742608 q^{68} +4.99375 q^{69} -4.38642 q^{70} -11.4831 q^{71} +1.00000 q^{72} +2.00000 q^{73} +11.2795 q^{74} -1.00000 q^{75} +6.16973 q^{76} -1.82659 q^{77} +3.21926 q^{78} -12.7580 q^{79} -1.00000 q^{80} +1.00000 q^{81} -1.15021 q^{82} -4.45478 q^{83} -4.38642 q^{84} -0.742608 q^{85} +11.2537 q^{86} +1.25739 q^{87} -0.416420 q^{88} +8.27692 q^{89} -1.00000 q^{90} -14.1210 q^{91} -4.99375 q^{92} -0.298097 q^{93} +4.99375 q^{94} -6.16973 q^{95} -1.00000 q^{96} +1.16326 q^{97} +12.2407 q^{98} -0.416420 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 5 q^{5} - 5 q^{6} + 3 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 5 * q^5 - 5 * q^6 + 3 * q^7 + 5 * q^8 + 5 * q^9	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 5 q^{5} - 5 q^{6} + 3 q^{7} + 5 q^{8} + 5 q^{9} - 5 q^{10} - 5 q^{12} + 7 q^{13} + 3 q^{14} + 5 q^{15} + 5 q^{16} + 5 q^{18} + 10 q^{19} - 5 q^{20} - 3 q^{21} - 4 q^{23} - 5 q^{24} + 5 q^{25} + 7 q^{26} - 5 q^{27} + 3 q^{28} - 10 q^{29} + 5 q^{30} + 7 q^{31} + 5 q^{32} - 3 q^{35} + 5 q^{36} + 16 q^{37} + 10 q^{38} - 7 q^{39} - 5 q^{40} - 4 q^{41} - 3 q^{42} + 14 q^{43} - 5 q^{45} - 4 q^{46} + 4 q^{47} - 5 q^{48} + 8 q^{49} + 5 q^{50} + 7 q^{52} - 3 q^{53} - 5 q^{54} + 3 q^{56} - 10 q^{57} - 10 q^{58} + 12 q^{59} + 5 q^{60} + 3 q^{61} + 7 q^{62} + 3 q^{63} + 5 q^{64} - 7 q^{65} + 24 q^{67} + 4 q^{69} - 3 q^{70} - 8 q^{71} + 5 q^{72} + 10 q^{73} + 16 q^{74} - 5 q^{75} + 10 q^{76} + 16 q^{77} - 7 q^{78} + 7 q^{79} - 5 q^{80} + 5 q^{81} - 4 q^{82} + 4 q^{83} - 3 q^{84} + 14 q^{86} + 10 q^{87} + 26 q^{89} - 5 q^{90} - 5 q^{91} - 4 q^{92} - 7 q^{93} + 4 q^{94} - 10 q^{95} - 5 q^{96} + 15 q^{97} + 8 q^{98}+O(q^{100}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 5 * q^5 - 5 * q^6 + 3 * q^7 + 5 * q^8 + 5 * q^9 - 5 * q^10 - 5 * q^12 + 7 * q^13 + 3 * q^14 + 5 * q^15 + 5 * q^16 + 5 * q^18 + 10 * q^19 - 5 * q^20 - 3 * q^21 - 4 * q^23 - 5 * q^24 + 5 * q^25 + 7 * q^26 - 5 * q^27 + 3 * q^28 - 10 * q^29 + 5 * q^30 + 7 * q^31 + 5 * q^32 - 3 * q^35 + 5 * q^36 + 16 * q^37 + 10 * q^38 - 7 * q^39 - 5 * q^40 - 4 * q^41 - 3 * q^42 + 14 * q^43 - 5 * q^45 - 4 * q^46 + 4 * q^47 - 5 * q^48 + 8 * q^49 + 5 * q^50 + 7 * q^52 - 3 * q^53 - 5 * q^54 + 3 * q^56 - 10 * q^57 - 10 * q^58 + 12 * q^59 + 5 * q^60 + 3 * q^61 + 7 * q^62 + 3 * q^63 + 5 * q^64 - 7 * q^65 + 24 * q^67 + 4 * q^69 - 3 * q^70 - 8 * q^71 + 5 * q^72 + 10 * q^73 + 16 * q^74 - 5 * q^75 + 10 * q^76 + 16 * q^77 - 7 * q^78 + 7 * q^79 - 5 * q^80 + 5 * q^81 - 4 * q^82 + 4 * q^83 - 3 * q^84 + 14 * q^86 + 10 * q^87 + 26 * q^89 - 5 * q^90 - 5 * q^91 - 4 * q^92 - 7 * q^93 + 4 * q^94 - 10 * q^95 - 5 * q^96 + 15 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	4.38642	1.65791	0.828955	−	0.559315i	$-0.188936\pi$
$7$	4.38642	1.65791	0.828955	+	0.559315i	$0.188936\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−0.416420	−0.125555	−0.0627777	−	0.998028i	$-0.519996\pi$
$11$	−0.416420	−0.125555	−0.0627777	+	0.998028i	$0.519996\pi$
$12$	−1.00000	−0.288675
$13$	−3.21926	−0.892862	−0.446431	−	0.894818i	$-0.647305\pi$
$13$	−3.21926	−0.892862	−0.446431	+	0.894818i	$0.647305\pi$
$14$	4.38642	1.17232
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0.742608	0.180109	0.0900545	−	0.995937i	$-0.471296\pi$
$17$	0.742608	0.180109	0.0900545	+	0.995937i	$0.471296\pi$
$18$	1.00000	0.235702
$19$	6.16973	1.41543	0.707717	−	0.706496i	$-0.249725\pi$
$19$	6.16973	1.41543	0.707717	+	0.706496i	$0.249725\pi$
$20$	−1.00000	−0.223607
$21$	−4.38642	−0.957195
$22$	−0.416420	−0.0887811
$23$	−4.99375	−1.04127	−0.520635	−	0.853779i	$-0.674305\pi$
$23$	−4.99375	−1.04127	−0.520635	+	0.853779i	$0.674305\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−3.21926	−0.631349
$27$	−1.00000	−0.192450
$28$	4.38642	0.828955
$29$	−1.25739	−0.233492	−0.116746	−	0.993162i	$-0.537246\pi$
$29$	−1.25739	−0.233492	−0.116746	+	0.993162i	$0.537246\pi$
$30$	1.00000	0.182574
$31$	0.298097	0.0535399	0.0267699	−	0.999642i	$-0.491478\pi$
$31$	0.298097	0.0535399	0.0267699	+	0.999642i	$0.491478\pi$
$32$	1.00000	0.176777
$33$	0.416420	0.0724895
$34$	0.742608	0.127356
$35$	−4.38642	−0.741440
$36$	1.00000	0.166667
$37$	11.2795	1.85434	0.927168	−	0.374645i	$-0.122235\pi$
$37$	11.2795	1.85434	0.927168	+	0.374645i	$0.122235\pi$
$38$	6.16973	1.00086
$39$	3.21926	0.515494
$40$	−1.00000	−0.158114
$41$	−1.15021	−0.179632	−0.0898162	−	0.995958i	$-0.528628\pi$
$41$	−1.15021	−0.179632	−0.0898162	+	0.995958i	$0.528628\pi$
$42$	−4.38642	−0.676839
$43$	11.2537	1.71618	0.858088	−	0.513503i	$-0.171652\pi$
$43$	11.2537	1.71618	0.858088	+	0.513503i	$0.171652\pi$
$44$	−0.416420	−0.0627777
$45$	−1.00000	−0.149071
$46$	−4.99375	−0.736289
$47$	4.99375	0.728414	0.364207	−	0.931318i	$-0.381340\pi$
$47$	4.99375	0.728414	0.364207	+	0.931318i	$0.381340\pi$
$48$	−1.00000	−0.144338
$49$	12.2407	1.74867
$50$	1.00000	0.141421
$51$	−0.742608	−0.103986
$52$	−3.21926	−0.446431
$53$	1.72522	0.236977	0.118489	−	0.992955i	$-0.462195\pi$
$53$	1.72522	0.236977	0.118489	+	0.992955i	$0.462195\pi$
$54$	−1.00000	−0.136083
$55$	0.416420	0.0561501
$56$	4.38642	0.586160
$57$	−6.16973	−0.817201
$58$	−1.25739	−0.165104
$59$	3.60122	0.468839	0.234419	−	0.972136i	$-0.424681\pi$
$59$	3.60122	0.468839	0.234419	+	0.972136i	$0.424681\pi$
$60$	1.00000	0.129099
$61$	0.959294	0.122825	0.0614125	−	0.998112i	$-0.480439\pi$
$61$	0.959294	0.122825	0.0614125	+	0.998112i	$0.480439\pi$
$62$	0.298097	0.0378584
$63$	4.38642	0.552637
$64$	1.00000	0.125000
$65$	3.21926	0.399300
$66$	0.416420	0.0512578
$67$	−14.6297	−1.78730	−0.893649	−	0.448767i	$-0.851863\pi$
$67$	−14.6297	−1.78730	−0.893649	+	0.448767i	$0.851863\pi$
$68$	0.742608	0.0900545
$69$	4.99375	0.601177
$70$	−4.38642	−0.524277
$71$	−11.4831	−1.36280	−0.681398	−	0.731913i	$-0.738628\pi$
$71$	−11.4831	−1.36280	−0.681398	+	0.731913i	$0.738628\pi$
$72$	1.00000	0.117851
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	11.2795	1.31121
$75$	−1.00000	−0.115470
$76$	6.16973	0.707717
$77$	−1.82659	−0.208160
$78$	3.21926	0.364509
$79$	−12.7580	−1.43539	−0.717695	−	0.696358i	$-0.754803\pi$
$79$	−12.7580	−1.43539	−0.717695	+	0.696358i	$0.754803\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−1.15021	−0.127019
$83$	−4.45478	−0.488976	−0.244488	−	0.969652i	$-0.578620\pi$
$83$	−4.45478	−0.488976	−0.244488	+	0.969652i	$0.578620\pi$
$84$	−4.38642	−0.478597
$85$	−0.742608	−0.0805472
$86$	11.2537	1.21352
$87$	1.25739	0.134807
$88$	−0.416420	−0.0443906
$89$	8.27692	0.877351	0.438676	−	0.898645i	$-0.355448\pi$
$89$	8.27692	0.877351	0.438676	+	0.898645i	$0.355448\pi$
$90$	−1.00000	−0.105409
$91$	−14.1210	−1.48028
$92$	−4.99375	−0.520635
$93$	−0.298097	−0.0309113
$94$	4.99375	0.515066
$95$	−6.16973	−0.633001
$96$	−1.00000	−0.102062
$97$	1.16326	0.118111	0.0590556	−	0.998255i	$-0.481191\pi$
$97$	1.16326	0.118111	0.0590556	+	0.998255i	$0.481191\pi$
$98$	12.2407	1.23649
$99$	−0.416420	−0.0418518
$100$	1.00000	0.100000
$101$	−2.65451	−0.264134	−0.132067	−	0.991241i	$-0.542161\pi$
$101$	−2.65451	−0.264134	−0.132067	+	0.991241i	$0.542161\pi$
$102$	−0.742608	−0.0735292
$103$	−6.98585	−0.688336	−0.344168	−	0.938908i	$-0.611839\pi$
$103$	−6.98585	−0.688336	−0.344168	+	0.938908i	$0.611839\pi$
$104$	−3.21926	−0.315674
$105$	4.38642	0.428071
$106$	1.72522	0.167568
$107$	−0.225506	−0.0218005	−0.0109002	−	0.999941i	$-0.503470\pi$
$107$	−0.225506	−0.0218005	−0.0109002	+	0.999941i	$0.503470\pi$
$108$	−1.00000	−0.0962250
$109$	10.4747	1.00330	0.501649	−	0.865071i	$-0.332727\pi$
$109$	10.4747	1.00330	0.501649	+	0.865071i	$0.332727\pi$
$110$	0.416420	0.0397041
$111$	−11.2795	−1.07060
$112$	4.38642	0.414478
$113$	8.62874	0.811724	0.405862	−	0.913934i	$-0.366971\pi$
$113$	8.62874	0.811724	0.405862	+	0.913934i	$0.366971\pi$
$114$	−6.16973	−0.577848
$115$	4.99375	0.465670
$116$	−1.25739	−0.116746
$117$	−3.21926	−0.297621
$118$	3.60122	0.331519
$119$	3.25739	0.298605
$120$	1.00000	0.0912871
$121$	−10.8266	−0.984236
$122$	0.959294	0.0868504
$123$	1.15021	0.103711
$124$	0.298097	0.0267699
$125$	−1.00000	−0.0894427
$126$	4.38642	0.390773
$127$	16.4127	1.45640	0.728198	−	0.685367i	$-0.240358\pi$
$127$	16.4127	1.45640	0.728198	+	0.685367i	$0.240358\pi$
$128$	1.00000	0.0883883
$129$	−11.2537	−0.990835
$130$	3.21926	0.282348
$131$	9.36903	0.818576	0.409288	−	0.912405i	$-0.365777\pi$
$131$	9.36903	0.818576	0.409288	+	0.912405i	$0.365777\pi$
$132$	0.416420	0.0362447
$133$	27.0630	2.34666
$134$	−14.6297	−1.26381
$135$	1.00000	0.0860663
$136$	0.742608	0.0636782
$137$	−1.00000	−0.0854358
$137$	−1.00000	−0.0854358
$138$	4.99375	0.425097
$139$	9.51736	0.807252	0.403626	−	0.914924i	$-0.367750\pi$
$139$	9.51736	0.807252	0.403626	+	0.914924i	$0.367750\pi$
$140$	−4.38642	−0.370720
$141$	−4.99375	−0.420550
$142$	−11.4831	−0.963642
$143$	1.34057	0.112104
$144$	1.00000	0.0833333
$145$	1.25739	0.104421
$146$	2.00000	0.165521
$147$	−12.2407	−1.00959
$148$	11.2795	0.927168
$149$	15.7987	1.29428	0.647141	−	0.762370i	$-0.275964\pi$
$149$	15.7987	1.29428	0.647141	+	0.762370i	$0.275964\pi$
$150$	−1.00000	−0.0816497
$151$	19.0784	1.55258	0.776289	−	0.630377i	$-0.217100\pi$
$151$	19.0784	1.55258	0.776289	+	0.630377i	$0.217100\pi$
$152$	6.16973	0.500431
$153$	0.742608	0.0600363
$154$	−1.82659	−0.147191
$155$	−0.298097	−0.0239438
$156$	3.21926	0.257747
$157$	19.1319	1.52689	0.763444	−	0.645874i	$-0.223507\pi$
$157$	19.1319	1.52689	0.763444	+	0.645874i	$0.223507\pi$
$158$	−12.7580	−1.01497
$159$	−1.72522	−0.136819
$160$	−1.00000	−0.0790569
$161$	−21.9047	−1.72633
$162$	1.00000	0.0785674
$163$	−0.772837	−0.0605333	−0.0302666	−	0.999542i	$-0.509636\pi$
$163$	−0.772837	−0.0605333	−0.0302666	+	0.999542i	$0.509636\pi$
$164$	−1.15021	−0.0898162
$165$	−0.416420	−0.0324183
$166$	−4.45478	−0.345758
$167$	8.72780	0.675377	0.337689	−	0.941258i	$-0.390355\pi$
$167$	8.72780	0.675377	0.337689	+	0.941258i	$0.390355\pi$
$168$	−4.38642	−0.338420
$169$	−2.63637	−0.202798
$170$	−0.742608	−0.0569555
$171$	6.16973	0.471811
$172$	11.2537	0.858088
$173$	16.4385	1.24980	0.624899	−	0.780706i	$-0.285140\pi$
$173$	16.4385	1.24980	0.624899	+	0.780706i	$0.285140\pi$
$174$	1.25739	0.0953226
$175$	4.38642	0.331582
$176$	−0.416420	−0.0313889
$177$	−3.60122	−0.270684
$178$	8.27692	0.620381
$179$	22.2996	1.66675	0.833374	−	0.552709i	$-0.186406\pi$
$179$	22.2996	1.66675	0.833374	+	0.552709i	$0.186406\pi$
$180$	−1.00000	−0.0745356
$181$	14.9947	1.11455	0.557273	−	0.830330i	$-0.311848\pi$
$181$	14.9947	1.11455	0.557273	+	0.830330i	$0.311848\pi$
$182$	−14.1210	−1.04672
$183$	−0.959294	−0.0709131
$184$	−4.99375	−0.368144
$185$	−11.2795	−0.829285
$186$	−0.298097	−0.0218576
$187$	−0.309237	−0.0226137
$188$	4.99375	0.364207
$189$	−4.38642	−0.319065
$190$	−6.16973	−0.447599
$191$	−4.91392	−0.355559	−0.177779	−	0.984070i	$-0.556891\pi$
$191$	−4.91392	−0.355559	−0.177779	+	0.984070i	$0.556891\pi$
$192$	−1.00000	−0.0721688
$193$	−8.01965	−0.577267	−0.288633	−	0.957440i	$-0.593201\pi$
$193$	−8.01965	−0.577267	−0.288633	+	0.957440i	$0.593201\pi$
$194$	1.16326	0.0835172
$195$	−3.21926	−0.230536
$196$	12.2407	0.874333
$197$	−2.34138	−0.166816	−0.0834081	−	0.996515i	$-0.526581\pi$
$197$	−2.34138	−0.166816	−0.0834081	+	0.996515i	$0.526581\pi$
$198$	−0.416420	−0.0295937
$199$	−3.26486	−0.231440	−0.115720	−	0.993282i	$-0.536917\pi$
$199$	−3.26486	−0.231440	−0.115720	+	0.993282i	$0.536917\pi$
$200$	1.00000	0.0707107
$201$	14.6297	1.03190
$202$	−2.65451	−0.186771
$203$	−5.51545	−0.387108
$204$	−0.742608	−0.0519930
$205$	1.15021	0.0803340
$206$	−6.98585	−0.486727
$207$	−4.99375	−0.347090
$208$	−3.21926	−0.223215
$209$	−2.56920	−0.177715
$210$	4.38642	0.302692
$211$	−3.23922	−0.222997	−0.111499	−	0.993765i	$-0.535565\pi$
$211$	−3.23922	−0.222997	−0.111499	+	0.993765i	$0.535565\pi$
$212$	1.72522	0.118489
$213$	11.4831	0.786811
$214$	−0.225506	−0.0154153
$215$	−11.2537	−0.767497
$216$	−1.00000	−0.0680414
$217$	1.30758	0.0887643
$218$	10.4747	0.709439
$219$	−2.00000	−0.135147
$220$	0.416420	0.0280751
$221$	−2.39065	−0.160812
$222$	−11.2795	−0.757030
$223$	16.6289	1.11355	0.556776	−	0.830663i	$-0.312038\pi$
$223$	16.6289	1.11355	0.556776	+	0.830663i	$0.312038\pi$
$224$	4.38642	0.293080
$225$	1.00000	0.0666667
$226$	8.62874	0.573975
$227$	18.6530	1.23804	0.619021	−	0.785375i	$-0.287530\pi$
$227$	18.6530	1.23804	0.619021	+	0.785375i	$0.287530\pi$
$228$	−6.16973	−0.408601
$229$	−7.40984	−0.489656	−0.244828	−	0.969567i	$-0.578732\pi$
$229$	−7.40984	−0.489656	−0.244828	+	0.969567i	$0.578732\pi$
$230$	4.99375	0.329278
$231$	1.82659	0.120181
$232$	−1.25739	−0.0825518
$233$	−26.7222	−1.75063	−0.875315	−	0.483553i	$-0.839346\pi$
$233$	−26.7222	−1.75063	−0.875315	+	0.483553i	$0.839346\pi$
$234$	−3.21926	−0.210450
$235$	−4.99375	−0.325757
$236$	3.60122	0.234419
$237$	12.7580	0.828723
$238$	3.25739	0.211145
$239$	−9.83241	−0.636005	−0.318003	−	0.948090i	$-0.603012\pi$
$239$	−9.83241	−0.636005	−0.318003	+	0.948090i	$0.603012\pi$
$240$	1.00000	0.0645497
$241$	10.8050	0.696010	0.348005	−	0.937493i	$-0.386859\pi$
$241$	10.8050	0.696010	0.348005	+	0.937493i	$0.386859\pi$
$242$	−10.8266	−0.695960
$243$	−1.00000	−0.0641500
$244$	0.959294	0.0614125
$245$	−12.2407	−0.782028
$246$	1.15021	0.0733346
$247$	−19.8620	−1.26379
$248$	0.298097	0.0189292
$249$	4.45478	0.282310
$250$	−1.00000	−0.0632456
$251$	−10.3098	−0.650748	−0.325374	−	0.945585i	$-0.605490\pi$
$251$	−10.3098	−0.650748	−0.325374	+	0.945585i	$0.605490\pi$
$252$	4.38642	0.276318
$253$	2.07950	0.130737
$254$	16.4127	1.02983
$255$	0.742608	0.0465039
$256$	1.00000	0.0625000
$257$	−29.2239	−1.82294	−0.911470	−	0.411367i	$-0.865051\pi$
$257$	−29.2239	−1.82294	−0.911470	+	0.411367i	$0.865051\pi$
$258$	−11.2537	−0.700626
$259$	49.4766	3.07432
$260$	3.21926	0.199650
$261$	−1.25739	−0.0778306
$262$	9.36903	0.578821
$263$	21.9554	1.35383	0.676914	−	0.736062i	$-0.263317\pi$
$263$	21.9554	1.35383	0.676914	+	0.736062i	$0.263317\pi$
$264$	0.416420	0.0256289
$265$	−1.72522	−0.105980
$266$	27.0630	1.65934
$267$	−8.27692	−0.506539
$268$	−14.6297	−0.893649
$269$	−11.7861	−0.718614	−0.359307	−	0.933219i	$-0.616987\pi$
$269$	−11.7861	−0.718614	−0.359307	+	0.933219i	$0.616987\pi$
$270$	1.00000	0.0608581
$271$	4.81153	0.292279	0.146140	−	0.989264i	$-0.453315\pi$
$271$	4.81153	0.292279	0.146140	+	0.989264i	$0.453315\pi$
$272$	0.742608	0.0450273
$273$	14.1210	0.854643
$274$	−1.00000	−0.0604122
$275$	−0.416420	−0.0251111
$276$	4.99375	0.300589
$277$	−20.5972	−1.23757	−0.618783	−	0.785562i	$-0.712374\pi$
$277$	−20.5972	−1.23757	−0.618783	+	0.785562i	$0.712374\pi$
$278$	9.51736	0.570813
$279$	0.298097	0.0178466
$280$	−4.38642	−0.262139
$281$	−2.24177	−0.133733	−0.0668663	−	0.997762i	$-0.521300\pi$
$281$	−2.24177	−0.133733	−0.0668663	+	0.997762i	$0.521300\pi$
$282$	−4.99375	−0.297374
$283$	−10.6016	−0.630198	−0.315099	−	0.949059i	$-0.602038\pi$
$283$	−10.6016	−0.630198	−0.315099	+	0.949059i	$0.602038\pi$
$284$	−11.4831	−0.681398
$285$	6.16973	0.365463
$286$	1.34057	0.0792693
$287$	−5.04530	−0.297814
$288$	1.00000	0.0589256
$289$	−16.4485	−0.967561
$290$	1.25739	0.0738366
$291$	−1.16326	−0.0681915
$292$	2.00000	0.117041
$293$	−28.7288	−1.67835	−0.839177	−	0.543858i	$-0.816963\pi$
$293$	−28.7288	−1.67835	−0.839177	+	0.543858i	$0.816963\pi$
$294$	−12.2407	−0.713890
$295$	−3.60122	−0.209671
$296$	11.2795	0.655607
$297$	0.416420	0.0241632
$298$	15.7987	0.915196
$299$	16.0762	0.929710
$300$	−1.00000	−0.0577350
$301$	49.3635	2.84527
$302$	19.0784	1.09784
$303$	2.65451	0.152498
$304$	6.16973	0.353858
$305$	−0.959294	−0.0549290
$306$	0.742608	0.0424521
$307$	5.13553	0.293100	0.146550	−	0.989203i	$-0.453183\pi$
$307$	5.13553	0.293100	0.146550	+	0.989203i	$0.453183\pi$
$308$	−1.82659	−0.104080
$309$	6.98585	0.397411
$310$	−0.298097	−0.0169308
$311$	3.40395	0.193021	0.0965103	−	0.995332i	$-0.469232\pi$
$311$	3.40395	0.193021	0.0965103	+	0.995332i	$0.469232\pi$
$312$	3.21926	0.182255
$313$	9.09936	0.514326	0.257163	−	0.966368i	$-0.417212\pi$
$313$	9.09936	0.514326	0.257163	+	0.966368i	$0.417212\pi$
$314$	19.1319	1.07967
$315$	−4.38642	−0.247147
$316$	−12.7580	−0.717695
$317$	7.06303	0.396699	0.198350	−	0.980131i	$-0.436442\pi$
$317$	7.06303	0.396699	0.198350	+	0.980131i	$0.436442\pi$
$318$	−1.72522	−0.0967456
$319$	0.523603	0.0293162
$320$	−1.00000	−0.0559017
$321$	0.225506	0.0125865
$322$	−21.9047	−1.22070
$323$	4.58170	0.254932
$324$	1.00000	0.0555556
$325$	−3.21926	−0.178572
$326$	−0.772837	−0.0428035
$327$	−10.4747	−0.579254
$328$	−1.15021	−0.0635096
$329$	21.9047	1.20764
$330$	−0.416420	−0.0229232
$331$	−27.8751	−1.53215	−0.766077	−	0.642748i	$-0.777794\pi$
$331$	−27.8751	−1.53215	−0.766077	+	0.642748i	$0.777794\pi$
$332$	−4.45478	−0.244488
$333$	11.2795	0.618112
$334$	8.72780	0.477564
$335$	14.6297	0.799304
$336$	−4.38642	−0.239299
$337$	19.5807	1.06663	0.533314	−	0.845917i	$-0.320946\pi$
$337$	19.5807	1.06663	0.533314	+	0.845917i	$0.320946\pi$
$338$	−2.63637	−0.143400
$339$	−8.62874	−0.468649
$340$	−0.742608	−0.0402736
$341$	−0.124134	−0.00672223
$342$	6.16973	0.333621
$343$	22.9878	1.24122
$344$	11.2537	0.606760
$345$	−4.99375	−0.268855
$346$	16.4385	0.883740
$347$	−32.8478	−1.76336	−0.881681	−	0.471846i	$-0.843588\pi$
$347$	−32.8478	−1.76336	−0.881681	+	0.471846i	$0.843588\pi$
$348$	1.25739	0.0674033
$349$	−18.4089	−0.985405	−0.492703	−	0.870198i	$-0.663991\pi$
$349$	−18.4089	−0.985405	−0.492703	+	0.870198i	$0.663991\pi$
$350$	4.38642	0.234464
$351$	3.21926	0.171831
$352$	−0.416420	−0.0221953
$353$	23.2923	1.23972	0.619862	−	0.784711i	$-0.287189\pi$
$353$	23.2923	1.23972	0.619862	+	0.784711i	$0.287189\pi$
$354$	−3.60122	−0.191403
$355$	11.4831	0.609461
$356$	8.27692	0.438676
$357$	−3.25739	−0.172399
$358$	22.2996	1.17857
$359$	−0.873066	−0.0460786	−0.0230393	−	0.999735i	$-0.507334\pi$
$359$	−0.873066	−0.0460786	−0.0230393	+	0.999735i	$0.507334\pi$
$360$	−1.00000	−0.0527046
$361$	19.0656	1.00345
$362$	14.9947	0.788102
$363$	10.8266	0.568249
$364$	−14.1210	−0.740142
$365$	−2.00000	−0.104685
$366$	−0.959294	−0.0501431
$367$	−19.9169	−1.03965	−0.519827	−	0.854271i	$-0.674004\pi$
$367$	−19.9169	−1.03965	−0.519827	+	0.854271i	$0.674004\pi$
$368$	−4.99375	−0.260317
$369$	−1.15021	−0.0598775
$370$	−11.2795	−0.586393
$371$	7.56755	0.392887
$372$	−0.298097	−0.0154556
$373$	7.01070	0.363000	0.181500	−	0.983391i	$-0.441905\pi$
$373$	7.01070	0.363000	0.181500	+	0.983391i	$0.441905\pi$
$374$	−0.309237	−0.0159903
$375$	1.00000	0.0516398
$376$	4.99375	0.257533
$377$	4.04787	0.208476
$378$	−4.38642	−0.225613
$379$	−25.5118	−1.31045	−0.655226	−	0.755433i	$-0.727427\pi$
$379$	−25.5118	−1.31045	−0.655226	+	0.755433i	$0.727427\pi$
$380$	−6.16973	−0.316501
$381$	−16.4127	−0.840851
$382$	−4.91392	−0.251418
$383$	12.2683	0.626880	0.313440	−	0.949608i	$-0.398519\pi$
$383$	12.2683	0.626880	0.313440	+	0.949608i	$0.398519\pi$
$384$	−1.00000	−0.0510310
$385$	1.82659	0.0930919
$386$	−8.01965	−0.408189
$387$	11.2537	0.572059
$388$	1.16326	0.0590556
$389$	8.30255	0.420956	0.210478	−	0.977599i	$-0.432498\pi$
$389$	8.30255	0.420956	0.210478	+	0.977599i	$0.432498\pi$
$390$	−3.21926	−0.163014
$391$	−3.70840	−0.187542
$392$	12.2407	0.618247
$393$	−9.36903	−0.472605
$394$	−2.34138	−0.117957
$395$	12.7580	0.641926
$396$	−0.416420	−0.0209259
$397$	16.5193	0.829082	0.414541	−	0.910031i	$-0.363942\pi$
$397$	16.5193	0.829082	0.414541	+	0.910031i	$0.363942\pi$
$398$	−3.26486	−0.163653
$399$	−27.0630	−1.35485
$400$	1.00000	0.0500000
$401$	−24.3792	−1.21744	−0.608720	−	0.793385i	$-0.708317\pi$
$401$	−24.3792	−1.21744	−0.608720	+	0.793385i	$0.708317\pi$
$402$	14.6297	0.729661
$403$	−0.959653	−0.0478037
$404$	−2.65451	−0.132067
$405$	−1.00000	−0.0496904
$406$	−5.51545	−0.273727
$407$	−4.69701	−0.232822
$408$	−0.742608	−0.0367646
$409$	18.0396	0.892001	0.446001	−	0.895033i	$-0.352848\pi$
$409$	18.0396	0.892001	0.446001	+	0.895033i	$0.352848\pi$
$410$	1.15021	0.0568047
$411$	1.00000	0.0493264
$412$	−6.98585	−0.344168
$413$	15.7965	0.777293
$414$	−4.99375	−0.245430
$415$	4.45478	0.218677
$416$	−3.21926	−0.157837
$417$	−9.51736	−0.466067
$418$	−2.56920	−0.125664
$419$	10.2926	0.502829	0.251414	−	0.967880i	$-0.419104\pi$
$419$	10.2926	0.502829	0.251414	+	0.967880i	$0.419104\pi$
$420$	4.38642	0.214035
$421$	2.23488	0.108922	0.0544608	−	0.998516i	$-0.482656\pi$
$421$	2.23488	0.108922	0.0544608	+	0.998516i	$0.482656\pi$
$422$	−3.23922	−0.157683
$423$	4.99375	0.242805
$424$	1.72522	0.0837842
$425$	0.742608	0.0360218
$426$	11.4831	0.556359
$427$	4.20787	0.203633
$428$	−0.225506	−0.0109002
$429$	−1.34057	−0.0647231
$430$	−11.2537	−0.542702
$431$	27.7073	1.33461	0.667307	−	0.744782i	$-0.267447\pi$
$431$	27.7073	1.33461	0.667307	+	0.744782i	$0.267447\pi$
$432$	−1.00000	−0.0481125
$433$	−35.6443	−1.71296	−0.856478	−	0.516184i	$-0.827352\pi$
$433$	−35.6443	−1.71296	−0.856478	+	0.516184i	$0.827352\pi$
$434$	1.30758	0.0627659
$435$	−1.25739	−0.0602873
$436$	10.4747	0.501649
$437$	−30.8101	−1.47385
$438$	−2.00000	−0.0955637
$439$	−18.1572	−0.866598	−0.433299	−	0.901250i	$-0.642651\pi$
$439$	−18.1572	−0.866598	−0.433299	+	0.901250i	$0.642651\pi$
$440$	0.416420	0.0198521
$441$	12.2407	0.582889
$442$	−2.39065	−0.113712
$443$	0.703002	0.0334006	0.0167003	−	0.999861i	$-0.494684\pi$
$443$	0.703002	0.0334006	0.0167003	+	0.999861i	$0.494684\pi$
$444$	−11.2795	−0.535301
$445$	−8.27692	−0.392363
$446$	16.6289	0.787400
$447$	−15.7987	−0.747254
$448$	4.38642	0.207239
$449$	−23.2332	−1.09644	−0.548222	−	0.836333i	$-0.684695\pi$
$449$	−23.2332	−1.09644	−0.548222	+	0.836333i	$0.684695\pi$
$450$	1.00000	0.0471405
$451$	0.478970	0.0225538
$452$	8.62874	0.405862
$453$	−19.0784	−0.896381
$454$	18.6530	0.875428
$455$	14.1210	0.662004
$456$	−6.16973	−0.288924
$457$	15.3595	0.718487	0.359244	−	0.933244i	$-0.383035\pi$
$457$	15.3595	0.718487	0.359244	+	0.933244i	$0.383035\pi$
$458$	−7.40984	−0.346239
$459$	−0.742608	−0.0346620
$460$	4.99375	0.232835
$461$	−18.7326	−0.872465	−0.436232	−	0.899834i	$-0.643687\pi$
$461$	−18.7326	−0.872465	−0.436232	+	0.899834i	$0.643687\pi$
$462$	1.82659	0.0849808
$463$	−8.86980	−0.412214	−0.206107	−	0.978529i	$-0.566080\pi$
$463$	−8.86980	−0.412214	−0.206107	+	0.978529i	$0.566080\pi$
$464$	−1.25739	−0.0583729
$465$	0.298097	0.0138239
$466$	−26.7222	−1.23788
$467$	4.90620	0.227032	0.113516	−	0.993536i	$-0.463789\pi$
$467$	4.90620	0.227032	0.113516	+	0.993536i	$0.463789\pi$
$468$	−3.21926	−0.148810
$469$	−64.1718	−2.96318
$470$	−4.99375	−0.230345
$471$	−19.1319	−0.881549
$472$	3.60122	0.165760
$473$	−4.68628	−0.215475
$474$	12.7580	0.585995
$475$	6.16973	0.283087
$476$	3.25739	0.149302
$477$	1.72522	0.0789925
$478$	−9.83241	−0.449724
$479$	−26.9064	−1.22938	−0.614692	−	0.788767i	$-0.710720\pi$
$479$	−26.9064	−1.22938	−0.614692	+	0.788767i	$0.710720\pi$
$480$	1.00000	0.0456435
$481$	−36.3116	−1.65567
$482$	10.8050	0.492153
$483$	21.9047	0.996698
$484$	−10.8266	−0.492118
$485$	−1.16326	−0.0528209
$486$	−1.00000	−0.0453609
$487$	11.6466	0.527760	0.263880	−	0.964556i	$-0.414998\pi$
$487$	11.6466	0.527760	0.263880	+	0.964556i	$0.414998\pi$
$488$	0.959294	0.0434252
$489$	0.772837	0.0349489
$490$	−12.2407	−0.552977
$491$	−18.2563	−0.823895	−0.411947	−	0.911208i	$-0.635151\pi$
$491$	−18.2563	−0.823895	−0.411947	+	0.911208i	$0.635151\pi$
$492$	1.15021	0.0518554
$493$	−0.933750	−0.0420540
$494$	−19.8620	−0.893632
$495$	0.416420	0.0187167
$496$	0.298097	0.0133850
$497$	−50.3698	−2.25939
$498$	4.45478	0.199623
$499$	−9.46758	−0.423827	−0.211913	−	0.977288i	$-0.567969\pi$
$499$	−9.46758	−0.423827	−0.211913	+	0.977288i	$0.567969\pi$
$500$	−1.00000	−0.0447214
$501$	−8.72780	−0.389929
$502$	−10.3098	−0.460149
$503$	11.8494	0.528338	0.264169	−	0.964476i	$-0.414902\pi$
$503$	11.8494	0.528338	0.264169	+	0.964476i	$0.414902\pi$
$504$	4.38642	0.195387
$505$	2.65451	0.118124
$506$	2.07950	0.0924451
$507$	2.63637	0.117085
$508$	16.4127	0.728198
$509$	34.3682	1.52334	0.761671	−	0.647964i	$-0.224379\pi$
$509$	34.3682	1.52334	0.761671	+	0.647964i	$0.224379\pi$
$510$	0.742608	0.0328833
$511$	8.77284	0.388087
$512$	1.00000	0.0441942
$513$	−6.16973	−0.272400
$514$	−29.2239	−1.28901
$515$	6.98585	0.307833
$516$	−11.2537	−0.495417
$517$	−2.07950	−0.0914563
$518$	49.4766	2.17388
$519$	−16.4385	−0.721571
$520$	3.21926	0.141174
$521$	−19.1041	−0.836965	−0.418482	−	0.908225i	$-0.637438\pi$
$521$	−19.1041	−0.836965	−0.418482	+	0.908225i	$0.637438\pi$
$522$	−1.25739	−0.0550345
$523$	5.59293	0.244562	0.122281	−	0.992496i	$-0.460979\pi$
$523$	5.59293	0.244562	0.122281	+	0.992496i	$0.460979\pi$
$524$	9.36903	0.409288
$525$	−4.38642	−0.191439
$526$	21.9554	0.957301
$527$	0.221370	0.00964302
$528$	0.416420	0.0181224
$529$	1.93757	0.0842423
$530$	−1.72522	−0.0749389
$531$	3.60122	0.156280
$532$	27.0630	1.17333
$533$	3.70282	0.160387
$534$	−8.27692	−0.358177
$535$	0.225506	0.00974947
$536$	−14.6297	−0.631905
$537$	−22.2996	−0.962298
$538$	−11.7861	−0.508137
$539$	−5.09726	−0.219555
$540$	1.00000	0.0430331
$541$	−35.9526	−1.54572	−0.772862	−	0.634574i	$-0.781175\pi$
$541$	−35.9526	−1.54572	−0.772862	+	0.634574i	$0.781175\pi$
$542$	4.81153	0.206673
$543$	−14.9947	−0.643483
$544$	0.742608	0.0318391
$545$	−10.4747	−0.448689
$546$	14.1210	0.604324
$547$	7.37763	0.315444	0.157722	−	0.987484i	$-0.449585\pi$
$547$	7.37763	0.315444	0.157722	+	0.987484i	$0.449585\pi$
$548$	−1.00000	−0.0427179
$549$	0.959294	0.0409417
$550$	−0.416420	−0.0177562
$551$	−7.75777	−0.330492
$552$	4.99375	0.212548
$553$	−55.9620	−2.37975
$554$	−20.5972	−0.875091
$555$	11.2795	0.478788
$556$	9.51736	0.403626
$557$	−31.0941	−1.31750	−0.658750	−	0.752362i	$-0.728915\pi$
$557$	−31.0941	−1.31750	−0.658750	+	0.752362i	$0.728915\pi$
$558$	0.298097	0.0126195
$559$	−36.2286	−1.53231
$560$	−4.38642	−0.185360
$561$	0.309237	0.0130560
$562$	−2.24177	−0.0945632
$563$	2.43137	0.102470	0.0512349	−	0.998687i	$-0.483684\pi$
$563$	2.43137	0.102470	0.0512349	+	0.998687i	$0.483684\pi$
$564$	−4.99375	−0.210275
$565$	−8.62874	−0.363014
$566$	−10.6016	−0.445617
$567$	4.38642	0.184212
$568$	−11.4831	−0.481821
$569$	−6.10115	−0.255773	−0.127887	−	0.991789i	$-0.540819\pi$
$569$	−6.10115	−0.255773	−0.127887	+	0.991789i	$0.540819\pi$
$570$	6.16973	0.258422
$571$	−11.8870	−0.497457	−0.248728	−	0.968573i	$-0.580013\pi$
$571$	−11.8870	−0.497457	−0.248728	+	0.968573i	$0.580013\pi$
$572$	1.34057	0.0560518
$573$	4.91392	0.205282
$574$	−5.04530	−0.210587
$575$	−4.99375	−0.208254
$576$	1.00000	0.0416667
$577$	12.5675	0.523193	0.261596	−	0.965177i	$-0.415751\pi$
$577$	12.5675	0.523193	0.261596	+	0.965177i	$0.415751\pi$
$578$	−16.4485	−0.684169
$579$	8.01965	0.333285
$580$	1.25739	0.0522103
$581$	−19.5405	−0.810678
$582$	−1.16326	−0.0482187
$583$	−0.718418	−0.0297538
$584$	2.00000	0.0827606
$585$	3.21926	0.133100
$586$	−28.7288	−1.18678
$587$	34.4791	1.42311	0.711553	−	0.702633i	$-0.247992\pi$
$587$	34.4791	1.42311	0.711553	+	0.702633i	$0.247992\pi$
$588$	−12.2407	−0.504797
$589$	1.83918	0.0757822
$590$	−3.60122	−0.148260
$591$	2.34138	0.0963114
$592$	11.2795	0.463584
$593$	−7.10766	−0.291877	−0.145938	−	0.989294i	$-0.546620\pi$
$593$	−7.10766	−0.291877	−0.145938	+	0.989294i	$0.546620\pi$
$594$	0.416420	0.0170859
$595$	−3.25739	−0.133540
$596$	15.7987	0.647141
$597$	3.26486	0.133622
$598$	16.0762	0.657404
$599$	−23.8393	−0.974048	−0.487024	−	0.873389i	$-0.661918\pi$
$599$	−23.8393	−0.974048	−0.487024	+	0.873389i	$0.661918\pi$
$600$	−1.00000	−0.0408248
$601$	−37.2736	−1.52042	−0.760210	−	0.649677i	$-0.774904\pi$
$601$	−37.2736	−1.52042	−0.760210	+	0.649677i	$0.774904\pi$
$602$	49.3635	2.01191
$603$	−14.6297	−0.595766
$604$	19.0784	0.776289
$605$	10.8266	0.440164
$606$	2.65451	0.107832
$607$	−12.7180	−0.516209	−0.258105	−	0.966117i	$-0.583098\pi$
$607$	−12.7180	−0.516209	−0.258105	+	0.966117i	$0.583098\pi$
$608$	6.16973	0.250216
$609$	5.51545	0.223497
$610$	−0.959294	−0.0388407
$611$	−16.0762	−0.650373
$612$	0.742608	0.0300182
$613$	36.3477	1.46807	0.734034	−	0.679112i	$-0.237635\pi$
$613$	36.3477	1.46807	0.734034	+	0.679112i	$0.237635\pi$
$614$	5.13553	0.207253
$615$	−1.15021	−0.0463809
$616$	−1.82659	−0.0735956
$617$	−21.5467	−0.867437	−0.433719	−	0.901048i	$-0.642799\pi$
$617$	−21.5467	−0.867437	−0.433719	+	0.901048i	$0.642799\pi$
$618$	6.98585	0.281012
$619$	10.4005	0.418030	0.209015	−	0.977912i	$-0.432974\pi$
$619$	10.4005	0.418030	0.209015	+	0.977912i	$0.432974\pi$
$620$	−0.298097	−0.0119719
$621$	4.99375	0.200392
$622$	3.40395	0.136486
$623$	36.3060	1.45457
$624$	3.21926	0.128874
$625$	1.00000	0.0400000
$626$	9.09936	0.363683
$627$	2.56920	0.102604
$628$	19.1319	0.763444
$629$	8.37624	0.333983
$630$	−4.38642	−0.174759
$631$	−26.3233	−1.04791	−0.523957	−	0.851745i	$-0.675545\pi$
$631$	−26.3233	−1.04791	−0.523957	+	0.851745i	$0.675545\pi$
$632$	−12.7580	−0.507487
$633$	3.23922	0.128747
$634$	7.06303	0.280509
$635$	−16.4127	−0.651320
$636$	−1.72522	−0.0684095
$637$	−39.4059	−1.56132
$638$	0.523603	0.0207297
$639$	−11.4831	−0.454265
$640$	−1.00000	−0.0395285
$641$	−30.4795	−1.20387	−0.601934	−	0.798545i	$-0.705603\pi$
$641$	−30.4795	−1.20387	−0.601934	+	0.798545i	$0.705603\pi$
$642$	0.225506	0.00890001
$643$	−1.64560	−0.0648961	−0.0324480	−	0.999473i	$-0.510330\pi$
$643$	−1.64560	−0.0648961	−0.0324480	+	0.999473i	$0.510330\pi$
$644$	−21.9047	−0.863166
$645$	11.2537	0.443115
$646$	4.58170	0.180264
$647$	20.8346	0.819095	0.409547	−	0.912289i	$-0.365687\pi$
$647$	20.8346	0.819095	0.409547	+	0.912289i	$0.365687\pi$
$648$	1.00000	0.0392837
$649$	−1.49962	−0.0588653
$650$	−3.21926	−0.126270
$651$	−1.30758	−0.0512481
$652$	−0.772837	−0.0302666
$653$	−23.4791	−0.918809	−0.459404	−	0.888227i	$-0.651937\pi$
$653$	−23.4791	−0.918809	−0.459404	+	0.888227i	$0.651937\pi$
$654$	−10.4747	−0.409595
$655$	−9.36903	−0.366078
$656$	−1.15021	−0.0449081
$657$	2.00000	0.0780274
$658$	21.9047	0.853934
$659$	0.533513	0.0207827	0.0103914	−	0.999946i	$-0.496692\pi$
$659$	0.533513	0.0207827	0.0103914	+	0.999946i	$0.496692\pi$
$660$	−0.416420	−0.0162091
$661$	−16.1772	−0.629218	−0.314609	−	0.949221i	$-0.601873\pi$
$661$	−16.1772	−0.629218	−0.314609	+	0.949221i	$0.601873\pi$
$662$	−27.8751	−1.08340
$663$	2.39065	0.0928451
$664$	−4.45478	−0.172879
$665$	−27.0630	−1.04946
$666$	11.2795	0.437071
$667$	6.27910	0.243128
$668$	8.72780	0.337689
$669$	−16.6289	−0.642909
$670$	14.6297	0.565193
$671$	−0.399470	−0.0154214
$672$	−4.38642	−0.169210
$673$	−5.34614	−0.206078	−0.103039	−	0.994677i	$-0.532857\pi$
$673$	−5.34614	−0.206078	−0.103039	+	0.994677i	$0.532857\pi$
$674$	19.5807	0.754220
$675$	−1.00000	−0.0384900
$676$	−2.63637	−0.101399
$677$	30.3093	1.16488	0.582441	−	0.812873i	$-0.302098\pi$
$677$	30.3093	1.16488	0.582441	+	0.812873i	$0.302098\pi$
$678$	−8.62874	−0.331385
$679$	5.10254	0.195818
$680$	−0.742608	−0.0284777
$681$	−18.6530	−0.714784
$682$	−0.124134	−0.00475333
$683$	12.3721	0.473404	0.236702	−	0.971582i	$-0.423933\pi$
$683$	12.3721	0.473404	0.236702	+	0.971582i	$0.423933\pi$
$684$	6.16973	0.235906
$685$	1.00000	0.0382080
$686$	22.9878	0.877677
$687$	7.40984	0.282703
$688$	11.2537	0.429044
$689$	−5.55394	−0.211588
$690$	−4.99375	−0.190109
$691$	22.9338	0.872442	0.436221	−	0.899840i	$-0.356317\pi$
$691$	22.9338	0.872442	0.436221	+	0.899840i	$0.356317\pi$
$692$	16.4385	0.624899
$693$	−1.82659	−0.0693866
$694$	−32.8478	−1.24689
$695$	−9.51736	−0.361014
$696$	1.25739	0.0476613
$697$	−0.854155	−0.0323534
$698$	−18.4089	−0.696787
$699$	26.7222	1.01073
$700$	4.38642	0.165791
$701$	21.6236	0.816714	0.408357	−	0.912822i	$-0.366102\pi$
$701$	21.6236	0.816714	0.408357	+	0.912822i	$0.366102\pi$
$702$	3.21926	0.121503
$703$	69.5914	2.62469
$704$	−0.416420	−0.0156944
$705$	4.99375	0.188076
$706$	23.2923	0.876617
$707$	−11.6438	−0.437911
$708$	−3.60122	−0.135342
$709$	0.835111	0.0313633	0.0156816	−	0.999877i	$-0.495008\pi$
$709$	0.835111	0.0313633	0.0156816	+	0.999877i	$0.495008\pi$
$710$	11.4831	0.430954
$711$	−12.7580	−0.478463
$712$	8.27692	0.310191
$713$	−1.48863	−0.0557495
$714$	−3.25739	−0.121905
$715$	−1.34057	−0.0501343
$716$	22.2996	0.833374
$717$	9.83241	0.367198
$718$	−0.873066	−0.0325825
$719$	−38.4953	−1.43563	−0.717816	−	0.696233i	$-0.754858\pi$
$719$	−38.4953	−1.43563	−0.717816	+	0.696233i	$0.754858\pi$
$720$	−1.00000	−0.0372678
$721$	−30.6429	−1.14120
$722$	19.0656	0.709548
$723$	−10.8050	−0.401841
$724$	14.9947	0.557273
$725$	−1.25739	−0.0466983
$726$	10.8266	0.401813
$727$	−13.5925	−0.504117	−0.252058	−	0.967712i	$-0.581108\pi$
$727$	−13.5925	−0.504117	−0.252058	+	0.967712i	$0.581108\pi$
$728$	−14.1210	−0.523360
$729$	1.00000	0.0370370
$730$	−2.00000	−0.0740233
$731$	8.35711	0.309099
$732$	−0.959294	−0.0354565
$733$	25.9888	0.959918	0.479959	−	0.877291i	$-0.340652\pi$
$733$	25.9888	0.959918	0.479959	+	0.877291i	$0.340652\pi$
$734$	−19.9169	−0.735147
$735$	12.2407	0.451504
$736$	−4.99375	−0.184072
$737$	6.09209	0.224405
$738$	−1.15021	−0.0423398
$739$	12.3989	0.456102	0.228051	−	0.973649i	$-0.426765\pi$
$739$	12.3989	0.456102	0.228051	+	0.973649i	$0.426765\pi$
$740$	−11.2795	−0.414642
$741$	19.8620	0.729648
$742$	7.56755	0.277813
$743$	−4.02419	−0.147633	−0.0738166	−	0.997272i	$-0.523518\pi$
$743$	−4.02419	−0.147633	−0.0738166	+	0.997272i	$0.523518\pi$
$744$	−0.298097	−0.0109288
$745$	−15.7987	−0.578821
$746$	7.01070	0.256680
$747$	−4.45478	−0.162992
$748$	−0.309237	−0.0113068
$749$	−0.989164	−0.0361433
$750$	1.00000	0.0365148
$751$	22.1972	0.809988	0.404994	−	0.914319i	$-0.367274\pi$
$751$	22.1972	0.809988	0.404994	+	0.914319i	$0.367274\pi$
$752$	4.99375	0.182103
$753$	10.3098	0.375710
$754$	4.04787	0.147415
$755$	−19.0784	−0.694334
$756$	−4.38642	−0.159532
$757$	32.4663	1.18001	0.590004	−	0.807400i	$-0.299126\pi$
$757$	32.4663	1.18001	0.590004	+	0.807400i	$0.299126\pi$
$758$	−25.5118	−0.926629
$759$	−2.07950	−0.0754811
$760$	−6.16973	−0.223800
$761$	34.9879	1.26831	0.634154	−	0.773206i	$-0.281348\pi$
$761$	34.9879	1.26831	0.634154	+	0.773206i	$0.281348\pi$
$762$	−16.4127	−0.594571
$763$	45.9466	1.66338
$764$	−4.91392	−0.177779
$765$	−0.742608	−0.0268491
$766$	12.2683	0.443271
$767$	−11.5933	−0.418608
$768$	−1.00000	−0.0360844
$769$	−29.4460	−1.06185	−0.530925	−	0.847419i	$-0.678155\pi$
$769$	−29.4460	−1.06185	−0.530925	+	0.847419i	$0.678155\pi$
$770$	1.82659	0.0658259
$771$	29.2239	1.05247
$772$	−8.01965	−0.288633
$773$	−20.0623	−0.721591	−0.360796	−	0.932645i	$-0.617495\pi$
$773$	−20.0623	−0.721591	−0.360796	+	0.932645i	$0.617495\pi$
$774$	11.2537	0.404507
$775$	0.298097	0.0107080
$776$	1.16326	0.0417586
$777$	−49.4766	−1.77496
$778$	8.30255	0.297661
$779$	−7.09648	−0.254258
$780$	−3.21926	−0.115268
$781$	4.78181	0.171107
$782$	−3.70840	−0.132612
$783$	1.25739	0.0449355
$784$	12.2407	0.437167
$785$	−19.1319	−0.682845
$786$	−9.36903	−0.334182
$787$	−4.53042	−0.161492	−0.0807460	−	0.996735i	$-0.525730\pi$
$787$	−4.53042	−0.161492	−0.0807460	+	0.996735i	$0.525730\pi$
$788$	−2.34138	−0.0834081
$789$	−21.9554	−0.781633
$790$	12.7580	0.453910
$791$	37.8493	1.34577
$792$	−0.416420	−0.0147969
$793$	−3.08822	−0.109666
$794$	16.5193	0.586249
$795$	1.72522	0.0611873
$796$	−3.26486	−0.115720
$797$	38.5397	1.36515	0.682573	−	0.730818i	$-0.260861\pi$
$797$	38.5397	1.36515	0.682573	+	0.730818i	$0.260861\pi$
$798$	−27.0630	−0.958021
$799$	3.70840	0.131194
$800$	1.00000	0.0353553
$801$	8.27692	0.292450
$802$	−24.3792	−0.860860
$803$	−0.832841	−0.0293903
$804$	14.6297	0.515948
$805$	21.9047	0.772039
$806$	−0.959653	−0.0338023
$807$	11.7861	0.414892
$808$	−2.65451	−0.0933855
$809$	−39.8858	−1.40231	−0.701156	−	0.713008i	$-0.747332\pi$
$809$	−39.8858	−1.40231	−0.701156	+	0.713008i	$0.747332\pi$
$810$	−1.00000	−0.0351364
$811$	20.5034	0.719971	0.359985	−	0.932958i	$-0.382782\pi$
$811$	20.5034	0.719971	0.359985	+	0.932958i	$0.382782\pi$
$812$	−5.51545	−0.193554
$813$	−4.81153	−0.168748
$814$	−4.69701	−0.164630
$815$	0.772837	0.0270713
$816$	−0.742608	−0.0259965
$817$	69.4324	2.42913
$818$	18.0396	0.630740
$819$	−14.1210	−0.493428
$820$	1.15021	0.0401670
$821$	−29.2378	−1.02041	−0.510204	−	0.860054i	$-0.670430\pi$
$821$	−29.2378	−1.02041	−0.510204	+	0.860054i	$0.670430\pi$
$822$	1.00000	0.0348790
$823$	32.8054	1.14352	0.571762	−	0.820419i	$-0.306260\pi$
$823$	32.8054	1.14352	0.571762	+	0.820419i	$0.306260\pi$
$824$	−6.98585	−0.243364
$825$	0.416420	0.0144979
$826$	15.7965	0.549629
$827$	−7.32167	−0.254599	−0.127300	−	0.991864i	$-0.540631\pi$
$827$	−7.32167	−0.254599	−0.127300	+	0.991864i	$0.540631\pi$
$828$	−4.99375	−0.173545
$829$	−10.8631	−0.377290	−0.188645	−	0.982045i	$-0.560410\pi$
$829$	−10.8631	−0.377290	−0.188645	+	0.982045i	$0.560410\pi$
$830$	4.45478	0.154628
$831$	20.5972	0.714509
$832$	−3.21926	−0.111608
$833$	9.09002	0.314951
$834$	−9.51736	−0.329559
$835$	−8.72780	−0.302038
$836$	−2.56920	−0.0888577
$837$	−0.298097	−0.0103038
$838$	10.2926	0.355554
$839$	−44.4911	−1.53600	−0.768002	−	0.640447i	$-0.778749\pi$
$839$	−44.4911	−1.53600	−0.768002	+	0.640447i	$0.778749\pi$
$840$	4.38642	0.151346
$841$	−27.4190	−0.945482
$842$	2.23488	0.0770192
$843$	2.24177	0.0772105
$844$	−3.23922	−0.111499
$845$	2.63637	0.0906939
$846$	4.99375	0.171689
$847$	−47.4900	−1.63177
$848$	1.72522	0.0592444
$849$	10.6016	0.363845
$850$	0.742608	0.0254713
$851$	−56.3270	−1.93086
$852$	11.4831	0.393405
$853$	3.11042	0.106499	0.0532494	−	0.998581i	$-0.483042\pi$
$853$	3.11042	0.106499	0.0532494	+	0.998581i	$0.483042\pi$
$854$	4.20787	0.143990
$855$	−6.16973	−0.211000
$856$	−0.225506	−0.00770764
$857$	−1.56061	−0.0533094	−0.0266547	−	0.999645i	$-0.508485\pi$
$857$	−1.56061	−0.0533094	−0.0266547	+	0.999645i	$0.508485\pi$
$858$	−1.34057	−0.0457661
$859$	−30.8975	−1.05421	−0.527105	−	0.849800i	$-0.676723\pi$
$859$	−30.8975	−1.05421	−0.527105	+	0.849800i	$0.676723\pi$
$860$	−11.2537	−0.383749
$861$	5.04530	0.171943
$862$	27.7073	0.943715
$863$	−16.6260	−0.565957	−0.282979	−	0.959126i	$-0.591323\pi$
$863$	−16.6260	−0.565957	−0.282979	+	0.959126i	$0.591323\pi$
$864$	−1.00000	−0.0340207
$865$	−16.4385	−0.558926
$866$	−35.6443	−1.21124
$867$	16.4485	0.558621
$868$	1.30758	0.0443822
$869$	5.31270	0.180221
$870$	−1.25739	−0.0426296
$871$	47.0967	1.59581
$872$	10.4747	0.354719
$873$	1.16326	0.0393704
$874$	−30.8101	−1.04217
$875$	−4.38642	−0.148288
$876$	−2.00000	−0.0675737
$877$	20.2754	0.684651	0.342325	−	0.939581i	$-0.388785\pi$
$877$	20.2754	0.684651	0.342325	+	0.939581i	$0.388785\pi$
$878$	−18.1572	−0.612777
$879$	28.7288	0.968999
$880$	0.416420	0.0140375
$881$	−21.7136	−0.731551	−0.365776	−	0.930703i	$-0.619196\pi$
$881$	−21.7136	−0.731551	−0.365776	+	0.930703i	$0.619196\pi$
$882$	12.2407	0.412165
$883$	27.6924	0.931922	0.465961	−	0.884805i	$-0.345709\pi$
$883$	27.6924	0.931922	0.465961	+	0.884805i	$0.345709\pi$
$884$	−2.39065	−0.0804062
$885$	3.60122	0.121054
$886$	0.703002	0.0236178
$887$	−52.5511	−1.76449	−0.882247	−	0.470786i	$-0.843970\pi$
$887$	−52.5511	−1.76449	−0.882247	+	0.470786i	$0.843970\pi$
$888$	−11.2795	−0.378515
$889$	71.9932	2.41457
$890$	−8.27692	−0.277443
$891$	−0.416420	−0.0139506
$892$	16.6289	0.556776
$893$	30.8101	1.03102
$894$	−15.7987	−0.528389
$895$	−22.2996	−0.745392
$896$	4.38642	0.146540
$897$	−16.0762	−0.536768
$898$	−23.2332	−0.775303
$899$	−0.374825	−0.0125011
$900$	1.00000	0.0333333
$901$	1.28116	0.0426818
$902$	0.478970	0.0159480
$903$	−49.3635	−1.64272
$904$	8.62874	0.286988
$905$	−14.9947	−0.498440
$906$	−19.0784	−0.633837
$907$	20.0421	0.665488	0.332744	−	0.943017i	$-0.392025\pi$
$907$	20.0421	0.665488	0.332744	+	0.943017i	$0.392025\pi$
$908$	18.6530	0.619021
$909$	−2.65451	−0.0880447
$910$	14.1210	0.468107
$911$	39.7479	1.31691	0.658454	−	0.752621i	$-0.271211\pi$
$911$	39.7479	1.31691	0.658454	+	0.752621i	$0.271211\pi$
$912$	−6.16973	−0.204300
$913$	1.85506	0.0613936
$914$	15.3595	0.508047
$915$	0.959294	0.0317133
$916$	−7.40984	−0.244828
$917$	41.0965	1.35713
$918$	−0.742608	−0.0245097
$919$	25.2380	0.832524	0.416262	−	0.909245i	$-0.363340\pi$
$919$	25.2380	0.832524	0.416262	+	0.909245i	$0.363340\pi$
$920$	4.99375	0.164639
$921$	−5.13553	−0.169221
$922$	−18.7326	−0.616926
$923$	36.9672	1.21679
$924$	1.82659	0.0600905
$925$	11.2795	0.370867
$926$	−8.86980	−0.291480
$927$	−6.98585	−0.229445
$928$	−1.25739	−0.0412759
$929$	−18.0711	−0.592895	−0.296447	−	0.955049i	$-0.595802\pi$
$929$	−18.0711	−0.592895	−0.296447	+	0.955049i	$0.595802\pi$
$930$	0.298097	0.00977500
$931$	75.5216	2.47512
$932$	−26.7222	−0.875315
$933$	−3.40395	−0.111440
$934$	4.90620	0.160536
$935$	0.309237	0.0101131
$936$	−3.21926	−0.105225
$937$	−31.2437	−1.02069	−0.510344	−	0.859970i	$-0.670482\pi$
$937$	−31.2437	−1.02069	−0.510344	+	0.859970i	$0.670482\pi$
$938$	−64.1718	−2.09528
$939$	−9.09936	−0.296946
$940$	−4.99375	−0.162878
$941$	−25.9060	−0.844512	−0.422256	−	0.906477i	$-0.638762\pi$
$941$	−25.9060	−0.844512	−0.422256	+	0.906477i	$0.638762\pi$
$942$	−19.1319	−0.623350
$943$	5.74386	0.187046
$944$	3.60122	0.117210
$945$	4.38642	0.142690
$946$	−4.68628	−0.152364
$947$	−47.1779	−1.53308	−0.766538	−	0.642199i	$-0.778022\pi$
$947$	−47.1779	−1.53308	−0.766538	+	0.642199i	$0.778022\pi$
$948$	12.7580	0.414361
$949$	−6.43852	−0.209003
$950$	6.16973	0.200173
$951$	−7.06303	−0.229034
$952$	3.25739	0.105573
$953$	22.0340	0.713750	0.356875	−	0.934152i	$-0.383842\pi$
$953$	22.0340	0.713750	0.356875	+	0.934152i	$0.383842\pi$
$954$	1.72522	0.0558561
$955$	4.91392	0.159011
$956$	−9.83241	−0.318003
$957$	−0.523603	−0.0169257
$958$	−26.9064	−0.869306
$959$	−4.38642	−0.141645
$960$	1.00000	0.0322749
$961$	−30.9111	−0.997133
$962$	−36.3116	−1.17073
$963$	−0.225506	−0.00726683
$964$	10.8050	0.348005
$965$	8.01965	0.258162
$966$	21.9047	0.704772
$967$	−37.7342	−1.21345	−0.606725	−	0.794912i	$-0.707517\pi$
$967$	−37.7342	−1.21345	−0.606725	+	0.794912i	$0.707517\pi$
$968$	−10.8266	−0.347980
$969$	−4.58170	−0.147185
$970$	−1.16326	−0.0373500
$971$	−8.76886	−0.281406	−0.140703	−	0.990052i	$-0.544936\pi$
$971$	−8.76886	−0.281406	−0.140703	+	0.990052i	$0.544936\pi$
$972$	−1.00000	−0.0320750
$973$	41.7471	1.33835
$974$	11.6466	0.373182
$975$	3.21926	0.103099
$976$	0.959294	0.0307063
$977$	−34.6999	−1.11015	−0.555074	−	0.831801i	$-0.687310\pi$
$977$	−34.6999	−1.11015	−0.555074	+	0.831801i	$0.687310\pi$
$978$	0.772837	0.0247126
$979$	−3.44668	−0.110156
$980$	−12.2407	−0.391014
$981$	10.4747	0.334433
$982$	−18.2563	−0.582582
$983$	−16.8662	−0.537949	−0.268974	−	0.963147i	$-0.586685\pi$
$983$	−16.8662	−0.537949	−0.268974	+	0.963147i	$0.586685\pi$
$984$	1.15021	0.0366673
$985$	2.34138	0.0746025
$986$	−0.933750	−0.0297366
$987$	−21.9047	−0.697234
$988$	−19.8620	−0.631893
$989$	−56.1983	−1.78700
$990$	0.416420	0.0132347
$991$	−13.0245	−0.413737	−0.206868	−	0.978369i	$-0.566327\pi$
$991$	−13.0245	−0.413737	−0.206868	+	0.978369i	$0.566327\pi$
$992$	0.298097	0.00946460
$993$	27.8751	0.884590
$994$	−50.3698	−1.59763
$995$	3.26486	0.103503
$996$	4.45478	0.141155
$997$	29.2692	0.926965	0.463483	−	0.886106i	$-0.346600\pi$
$997$	29.2692	0.926965	0.463483	+	0.886106i	$0.346600\pi$
$998$	−9.46758	−0.299691
$999$	−11.2795	−0.356867

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4110.2.a.bb.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4110.2.a.bb.1.5	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4110 = 2 \cdot 3 \cdot 5 \cdot 137 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4110.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.38642 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +4.38642 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -0.416420 q^{11} -1.00000 q^{12} -3.21926 q^{13} +4.38642 q^{14} +1.00000 q^{15} +1.00000 q^{16} +0.742608 q^{17} +1.00000 q^{18} +6.16973 q^{19} -1.00000 q^{20} -4.38642 q^{21} -0.416420 q^{22} -4.99375 q^{23} -1.00000 q^{24} +1.00000 q^{25} -3.21926 q^{26} -1.00000 q^{27} +4.38642 q^{28} -1.25739 q^{29} +1.00000 q^{30} +0.298097 q^{31} +1.00000 q^{32} +0.416420 q^{33} +0.742608 q^{34} -4.38642 q^{35} +1.00000 q^{36} +11.2795 q^{37} +6.16973 q^{38} +3.21926 q^{39} -1.00000 q^{40} -1.15021 q^{41} -4.38642 q^{42} +11.2537 q^{43} -0.416420 q^{44} -1.00000 q^{45} -4.99375 q^{46} +4.99375 q^{47} -1.00000 q^{48} +12.2407 q^{49} +1.00000 q^{50} -0.742608 q^{51} -3.21926 q^{52} +1.72522 q^{53} -1.00000 q^{54} +0.416420 q^{55} +4.38642 q^{56} -6.16973 q^{57} -1.25739 q^{58} +3.60122 q^{59} +1.00000 q^{60} +0.959294 q^{61} +0.298097 q^{62} +4.38642 q^{63} +1.00000 q^{64} +3.21926 q^{65} +0.416420 q^{66} -14.6297 q^{67} +0.742608 q^{68} +4.99375 q^{69} -4.38642 q^{70} -11.4831 q^{71} +1.00000 q^{72} +2.00000 q^{73} +11.2795 q^{74} -1.00000 q^{75} +6.16973 q^{76} -1.82659 q^{77} +3.21926 q^{78} -12.7580 q^{79} -1.00000 q^{80} +1.00000 q^{81} -1.15021 q^{82} -4.45478 q^{83} -4.38642 q^{84} -0.742608 q^{85} +11.2537 q^{86} +1.25739 q^{87} -0.416420 q^{88} +8.27692 q^{89} -1.00000 q^{90} -14.1210 q^{91} -4.99375 q^{92} -0.298097 q^{93} +4.99375 q^{94} -6.16973 q^{95} -1.00000 q^{96} +1.16326 q^{97} +12.2407 q^{98} -0.416420 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 5 q^{5} - 5 q^{6} + 3 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 5 * q^5 - 5 * q^6 + 3 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} - 5 q^{5} - 5 q^{6} + 3 q^{7} + 5 q^{8} + 5 q^{9} - 5 q^{10} - 5 q^{12} + 7 q^{13} + 3 q^{14} + 5 q^{15} + 5 q^{16} + 5 q^{18} + 10 q^{19} - 5 q^{20} - 3 q^{21} - 4 q^{23} - 5 q^{24} + 5 q^{25} + 7 q^{26} - 5 q^{27} + 3 q^{28} - 10 q^{29} + 5 q^{30} + 7 q^{31} + 5 q^{32} - 3 q^{35} + 5 q^{36} + 16 q^{37} + 10 q^{38} - 7 q^{39} - 5 q^{40} - 4 q^{41} - 3 q^{42} + 14 q^{43} - 5 q^{45} - 4 q^{46} + 4 q^{47} - 5 q^{48} + 8 q^{49} + 5 q^{50} + 7 q^{52} - 3 q^{53} - 5 q^{54} + 3 q^{56} - 10 q^{57} - 10 q^{58} + 12 q^{59} + 5 q^{60} + 3 q^{61} + 7 q^{62} + 3 q^{63} + 5 q^{64} - 7 q^{65} + 24 q^{67} + 4 q^{69} - 3 q^{70} - 8 q^{71} + 5 q^{72} + 10 q^{73} + 16 q^{74} - 5 q^{75} + 10 q^{76} + 16 q^{77} - 7 q^{78} + 7 q^{79} - 5 q^{80} + 5 q^{81} - 4 q^{82} + 4 q^{83} - 3 q^{84} + 14 q^{86} + 10 q^{87} + 26 q^{89} - 5 q^{90} - 5 q^{91} - 4 q^{92} - 7 q^{93} + 4 q^{94} - 10 q^{95} - 5 q^{96} + 15 q^{97} + 8 q^{98}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 - 5 * q^5 - 5 * q^6 + 3 * q^7 + 5 * q^8 + 5 * q^9 - 5 * q^10 - 5 * q^12 + 7 * q^13 + 3 * q^14 + 5 * q^15 + 5 * q^16 + 5 * q^18 + 10 * q^19 - 5 * q^20 - 3 * q^21 - 4 * q^23 - 5 * q^24 + 5 * q^25 + 7 * q^26 - 5 * q^27 + 3 * q^28 - 10 * q^29 + 5 * q^30 + 7 * q^31 + 5 * q^32 - 3 * q^35 + 5 * q^36 + 16 * q^37 + 10 * q^38 - 7 * q^39 - 5 * q^40 - 4 * q^41 - 3 * q^42 + 14 * q^43 - 5 * q^45 - 4 * q^46 + 4 * q^47 - 5 * q^48 + 8 * q^49 + 5 * q^50 + 7 * q^52 - 3 * q^53 - 5 * q^54 + 3 * q^56 - 10 * q^57 - 10 * q^58 + 12 * q^59 + 5 * q^60 + 3 * q^61 + 7 * q^62 + 3 * q^63 + 5 * q^64 - 7 * q^65 + 24 * q^67 + 4 * q^69 - 3 * q^70 - 8 * q^71 + 5 * q^72 + 10 * q^73 + 16 * q^74 - 5 * q^75 + 10 * q^76 + 16 * q^77 - 7 * q^78 + 7 * q^79 - 5 * q^80 + 5 * q^81 - 4 * q^82 + 4 * q^83 - 3 * q^84 + 14 * q^86 + 10 * q^87 + 26 * q^89 - 5 * q^90 - 5 * q^91 - 4 * q^92 - 7 * q^93 + 4 * q^94 - 10 * q^95 - 5 * q^96 + 15 * q^97 + 8 * q^98

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